##
**Two consensus problems for discrete-time multi-agent systems with switching network topology.**
*(English)*
Zbl 1258.93015

Summary: In this paper, we study both the leaderless consensus problem and the leader-following consensus problem for linear discrete-time multi-agent systems under switching network topology. Under the assumption that the system matrix is marginally stable, we show that these two consensus problems can be solved via the state feedback protocols, provided that the dynamic graph is jointly connected. Our result will contain several existing results as special cases. The proof is based on the stability analysis of a class of linear discrete-time switched systems which may have some independent interest.

### MSC:

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

93B52 | Feedback control |

93C55 | Discrete-time control/observation systems |

### Keywords:

consensus; switching network; multi-agent systems; discrete-time systems; jointly connected dynamic graph
PDF
BibTeX
XML
Cite

\textit{Y. Su} and \textit{J. Huang}, Automatica 48, No. 9, 1988--1997 (2012; Zbl 1258.93015)

Full Text:
DOI

### References:

[1] | Ben-Israel, A.; Greville, T.N.E., Generalized inverse: theory and applications, (2003), Springer New York |

[2] | Bertsekas, D.P.; Tsitsiklis, J.N., Parall and distributed computation: numerical methods, (1989), Prentice Hall Englewood Cliffs, NJ |

[3] | Cheng, D.; Guo, L.; Huang, J., On quadratic Lyapunov function, IEEE transactions on automatic control, 48, 5, 885-890, (2003) · Zbl 1364.93557 |

[4] | Godsil, C.; Royle, G., Algebraic graph theory, (2001), Springer-Verlag New York · Zbl 0968.05002 |

[5] | Hong, Y.; Chen, G.; Bushnell, L., Distributed observers design for leader-following control of multi-agent networks, Automatica, 44, 3, 846-850, (2008) · Zbl 1283.93019 |

[6] | Hong, Y.; Gao, L.; Cheng, D.; Hu, J., Lyapunov-based approach to multiagent systems with switching jointly connected interconnection, IEEE transactions on automatic control, 52, 5, 943-948, (2007) · Zbl 1366.93437 |

[7] | Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 988-1001, (2003) · Zbl 1364.93514 |

[8] | Ji, Z.; Wang, Z.; Lin, H.; Wang, Z., Interconnection topologies for multi-agent coordination under leader-follower framework, Automatica, 45, 12, 2857-2863, (2009) · Zbl 1192.93013 |

[9] | Liberzon, D.; Morse, A.S., Basic problems in stability and design of switched system, IEEE control systems magazine, 19, 5, 59-70, (1999) · Zbl 1384.93064 |

[10] | Lin, Z. (2005). Coupled dynamic systems: from structure towards stability and stabilizability. Ph.D. dissertation. University of Toronto, Toronto, Canada. |

[11] | Nedić, A.; Olshevsky, A.; Ozdaglar, A.; Tsitsiklis, J.N., On distributed averaging algorithms and quantization effects, IEEE transactions on automatic control, 54, 11, 2506-2616, (2009) · Zbl 1367.93405 |

[12] | Ni, W.; Cheng, D., Leader-following consensus of multi-agent systems under fixed and switching topologies, Systems and control letters, 59, 3, 209-217, (2010) · Zbl 1223.93006 |

[13] | Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138 |

[14] | Olfati-Saber, R.; Murray, R.M., Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301 |

[15] | Qin, J.; Gao, H.; Zheng, W., Second-order consensus for multi-agent systems with switching topology and communication delay, Systems & control letters, 60, 6, 390-397, (2011) · Zbl 1225.93020 |

[16] | Qin, J.; Zheng, W.; Gao, H., Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology, Automatica, 47, 9, 1983-1991, (2011) · Zbl 1227.93011 |

[17] | Qu, Z., Cooperative control of dynamical systems: applications to autonomous vehicles, (2009), Springer Verlag London · Zbl 1171.93005 |

[18] | Ren, W., On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control, 53, 6, 1503-1509, (2008) · Zbl 1367.93567 |

[19] | Ren, W., Synchronization of coupled harmonic oscillators with local interaction, Automatica, 44, 2, 3195-3200, (2008) · Zbl 1153.93421 |

[20] | Ren, W.; Beard, R.W., () |

[21] | Ren, W.; Beard, R.W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE transactions on automatic control, 50, 5, 655-661, (2005) · Zbl 1365.93302 |

[22] | Scardovi, L.; Sepulchre, R., Synchronization in networks of identical linear systems, Automatica, 45, 11, 2557-2562, (2009) · Zbl 1183.93054 |

[23] | Shen, B.; Wang, Z.; Hung, Y.S., Distributed consensus \(H\)-infinity filtering in sensor networks with multiple missing measurements: the finite-horizon case, Automatica, 46, 10, 1682-1688, (2010) · Zbl 1204.93122 |

[24] | Su, Y.; Huang, J., Stability of a class of linear switching systems with applications to two consensus problems, IEEE transactions on automatic control, 57, 6, 1420-1430, (2012) · Zbl 1369.93387 |

[25] | Tsitsiklis, J.N. (1984). Problems in decentralized decision making and computation. Ph.D. thesis. Department of EECS, MIT, technical report LIDS-TH-1424, Laboratory for Information and Decision Systems, MIT. |

[26] | Tuna, S.E., Synchronizing linear systems via partial-state coupling, Automatica, 44, 8, 2179-2184, (2008) · Zbl 1283.93028 |

[27] | Wang, J.; Cheng, D.; Hu, X., Consensus of multi-agent linear dynamic systems, Asian journal of control, 10, 2, 144-155, (2008) |

[28] | Xu, J., Li, T., Xie, L., & Lum, K.Y. (2011). Dynamic consensus and formation: fixed and switching topologies. In Proceedings of 18th IFAC world congress (pp. 9188-9193). Milan, Italy, August 28-September 2. |

[29] | You, K.; Xie, L., Coordination of discrete-time multi-agent systems via relative output feedback, Internal journal of robust and nonlinear control, 21, 13, 1587-1605, (2011) · Zbl 1227.93013 |

[30] | You, K.; Xie, L., Network topology and communication data rate for consensusability of discrete-time multi-agent systems, IEEE transactions on automatic control, 56, 10, 2262-2275, (2011) · Zbl 1368.93014 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.